Search Loci: Convergence:
Mathematics is like checkers in being suitable for the young, not too difficult, amusing, and without peril to the state.
A Plague of Ratios
Remnants of a Book
Oxford, 2006. I've got Mercator's two notebooks in front of me. The paper is yellow with age, but it's intact and the writing is perfectly legible. The text is in Latin throughout, like that of Mercator's published prospectus, Rationes mathematicae ('mathematical ratios'). The first notebook is a real mess: it's been used from both ends, and although it started out with a fairly clear line of thought, Mercator kept getting distracted and jotting down odd pages of completely unrelated material. It's obvious that this was a working notebook, meant to be tidied up and sorted out fairly extensively before it could be published. The musical use of ratios is by far the most prominent topic in these notebooks, although the other subjects Mercator had listed in Rationes mathematicae are also represented here and there.
The other notebook seems at first to be the sorted-out version. It's in a neat hand, probably that of a scribe rather than Mercator himself. It's on good quality paper, and it's very clear and easy to read: even after three hundred years it's in good condition. But towards the middle of the book it gets less and less neat, and the calculations start to have rough working down the side of the page. Eventually this notebook, like the other one, trails off into a lot of rough notes on various different ideas, calculations which don't have much to do with the text, and so on. So at the time he came to England Mercator seems to have been having trouble putting this material in order.
But that's not all the manuscripts we have. It seems that Mercator made some other versions of the musical material, after he came to England. There are two versions; both are in English (slightly imperfect English, which suggests that the translation was done by Mercator himself, perhaps not that long after coming to England). There are manuscript copies of each in the Bodleian Library, Oxford; one of them was also copied out for Robert Hooke by one his assistants, and the copy is still in London. What seems to be the same text gets a mention in a book on music by the Fellow of the Royal Society William Holder in 1694: so it seems to have been passed around quite a bit. The thing that is most prominent in these later, English versions of the material is the use of logarithms to measure musical ratios.